How can I edit an action strip while seeing the global NLA animation playing?
If you select the strip in the NLA and press Tab, the action will open in the Dope Sheet and the other objects will continue to be animated.
The only problem is that the action you want to edit will stick to the beginning of the timeline, or at the frame where it is supposed to begin in the Dope Sheet as an action, not at the frame where the strip is placed in the NLA.
To make it begin at the same frame as in the NLA, enable the track pinning option: